0

Full Content is available to subscribers

Subscribe/Learn More  >

Time Optimal Transfer Function of a Mechanism in the Presence of Dissipative Forces

[+] Author Affiliations
A. A. Goun

Stanford University

O. K. Sliva

Southern Ural State University

Paper No. IMECE2004-61907, pp. 329-334; 6 pages
doi:10.1115/IMECE2004-61907
From:
  • ASME 2004 International Mechanical Engineering Congress and Exposition
  • Applied Mechanics
  • Anaheim, California, USA, November 13 – 19, 2004
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-4702-0 | eISBN: 0-7918-4178-2, 0-7918-4179-0, 0-7918-4180-4
  • Copyright © 2004 by ASME

abstract

A variety of optimization problems in theoretical mechanics are related to the problem of finding the quickest operating mechanism among all possible mechanisms. Let us consider a mechanical system with one degree of freedom consisting of leading and lagging links with masses M1 and M2 respectively. Source of mechanical energy is attached to the leading link and its potential energy is known as a function of the position of the leading link. Positions of the leading - x and lagging links - y are related through the position function. Now the optimization problem can be formulated in the following way: find the position function such that the lagging link is transferred from initial to the final position in the shortest time. The analytic solution for this problem for the case when dissipative forces can be neglected was found using variational calculus method. In the case when dissipative forces can be described as viscous friction the problem can be solved using iterative methods. The differential equation that describes the stationary point of these iterations was obtained. The dependence of the optimal position function on the magnitude of friction is analyzed. In the case when dissipative forces are of the dry friction type the approach based on the variational calculus fails. We were able to find the optimal position function problem using Maximum Principle. New qualitative features of the solution arising due to dry friction are discussed. Approaches developed in this paper can be generalized for a variety of mechanisms where the operating time is critical.

Copyright © 2004 by ASME

Figures

Tables

Interactive Graphics

Video

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In